J. Phys. Chem. 1985,89, 1329-1330
1
I
I
500
550 Wavelength I nm
I
600
Figure 3. Diffuse reflectance spectra of CdS powder (Furuuchi Chem.) as obtained (-); those obtained after grinding in an agate mortar for 5 (---) and 10 min (---).
per incident photon, observed at 436 nm is 28% at 30 O C and 35% at 60 OC, no correction being made for reflections from the flask and the photocatalyst. It is nearly constant at wavelengths shorter than 480 nm but drops to zero at wavelengths longer than 550 nm. The rate of hydrogen production under illumination by a solar simulator (AM1, 1.00 kW m-2) is 0.32 mol m-2 h-' a t 30 O C and 0.50 mol m-2 h-' at 70 OC. The quantum efficiency and the rate of hydrogen production are more than three times as high as those reported previously.' In the previous report,' we prepared the photocatlayst by grinding the CdS powder and platinum powder together in an
1329
agate mortar. It was later found that the efficiency of the photocatalyst decreases with increasing grinding time as shown in Figure 2. The reflectance spectrum of the well-ground CdS powder shows enhanced photoabsorption at wavelengths longer than that of band-gap excitation (520 nm) as shown in Figure 3. The photoluminescence of the CdS powder having a hexagonal crystal structure is weakened by grinding. These results show that the efficiency is decreased by grinding the CdS powder due to the formation of recombination centers. The high efficiency for hydrogen production observed with the annealed CdS powder may, therefore, be partly attributed to the removal of the defects formed during the manufacturing of the CdS powder. Generally, the grinding method is known to be useful for a Pt-loaded T i 0 2 p h o t ~ c a t a l y s t .For ~ ~ ~CdS, ~ however, the grinding process gives rise to an undesirable effect as shown in Figure 2. Both luminescence and absorption spectroscopic results show increased defects from grinding. Photodeposition of Pt on CdS powder from aqueous solutions of platinum(1V) hexachloride was also camed out in order to make damage-free photocatalysts. However, the efficiencies of the photocatalysts prepared by this method under various conditions were a little lower than those obtained by the photocatalysts prepared by the shaking method. The platinum powder (platinum black) used for the loading by the latter method has been manufactured for use as a hydrogenation catalyst and has a large surface area, ca. 50 mz g-'. The good results obtained may be attributed to this quality. Registry No. Hl,1333-74-0; CdS, 1306-23-6;Pt,7440-06-4; Na2S0,, 7757-83-1.
Stable Stationary States of Coupled Chemical Oscillators. Experlmental Evidence K. Bar-Eli* and S . Reuveni Department of Chemistry, Tel-Aviv University, Tel-Aviv, Israel 69978 (Received: July 19, 1984; In Final Form: February 5, 1985)
When chemical oscillators are coupled by mass transfer, they can, under appropriate conditions, stop oscillating and arrive at an inhomogeneous stable, stationary, steady state. This prediction is verified experimentally by coupling two Belousov-Zhabotinskii oscillators.
Introduction In previous it was shown that coupling chemical oscillators in a diffusionlike manner, Le., by a mass transfer which is proportional to the concentration difference between the coupled oscillators, may bring the whole system to an inhomogeneous stable, stationary steady state. This is a rather unexpected phenomenon, since intuitively we tend to think that the coupling or diffusion will tend to equalize and wash out the differences among the various parts of the system. Nevertheless, all tested mechanisms and models show that, when coupled under appropriate conditions, the oscillations will stop and a stable dissipative structure4 will be formed. The tested model oscillators were (1) the Brusselator due to prigogine and L e f e ~ e r(2) ; ~ an autocatalytic first-order decomposition due to K ~ m a r (3) ; ~ the Loth-Volterra prey-predator model;6 (4) the Noyes-Field-Thompson (NFT) (1) K. Bar-Eli, J . Phys. Chem., 88, 3636 (1984). (2) K. Bar-Eli, J . Phys. Chem., in press. (3) K. Bar-Eli, Physica D, in press. (4) I. Prigogine and R. Lefever, J. Chem. Phys., 48, 1695 (1968). ( 5 ) V. R. Kumar, V. K. Jayaraman, B. D. Kulkarni, and L. K. Doraiswamy, Chem. Eng. Sci., 38,673 (1983).
0022-3654/85/2089-1329$01.50/0
model' for the oxidation of cerous by bromate ions; (5) the Oregonator;8 and (6) the Field-Koros-Noyes (FKN) m e ~ h a n i s m . ~ The last two model the famous Belousov-Zhabotinskii (BZ)l0 oscillating reaction. It is striking that such diverse models which differ in their type of nonlinearity (e.g., Oregonator vs. Brusselator) and may be conservative or not (eg., Lotka-Volterra vs. the other mechanisms) all may be stabilized when coupled. The coupled oscillators may also work under the same constraints and still become stable. This was first shown by Prigogine and Lefever4 for the case of two coupled identical Brusselators. Bar-Eli3 has shown that this ( 6 ) (a) A. Lotka, J . Am. Chem. SOC.,42, 1595 (1920); (b) A. Lotka, J . Phys. Chem., 14, 271 (1910); (c) V. Volterra, 'Lecons sur la Theorie Mathematique de la Lutte pour la Vie", Gauthier-Villars, Paris, 1931. (7) R. M. Noyes, R. J. Field, and R. C. Thompson, J . Am. Chem. SOC., 93, 7315 (1971). (8) R. J. Field, and R. M. Noyes, J . Chem. Phys., 60,1877 (1974). (9) R. J. Field, E. Koros, and R. M. Noyes, J . Am. Chem. SOC.,94, 8649 (1972). (10) (a) B. P. Belousov, Sb. ReJ Radiat. Med., 1958, 145 (1959). (b) A. M. Zhabotinskii, Dokl. Akad. Nauk. SSSR, 157, 392 (1969); (c) A. M. Zhabotinskii, Biofirica, 9, 306 (1964); (d) A. N. Zaikin and A. M. Zhabotinskii, Nature (London), 225, 535 (1970).
0 1985 American Chemical Society
Letters
1330 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
TABLE I: Oscillationscand Steady States as a Function of the Coupling Rate
CSTR I Figure 1. Time-voltage plots of two CSTRs run in parallel: upward arrow, coupling is turned on; downward arrow, coupling is turned off. The time scanned between the arrows is about 0.5 h.
stability can be formed even when the coupling involves more than two oscillators. In this work we report an experimental verification of the abovementioned predictions, namely, that the coupled oscillators will come to a halt at a stable steady state provided the right coupling is applied. The tested system was the BZ reaction in which the oscillating regime is quite large, and there is no difficulty in obtaining the oscillations. The mechanism of the NFT oscillator seems to be simpler and better understood”J2 than the FKN or Oregonator mechanisms of the BZ reaction, but its oscillating regime is very small,” and thus the BZ oscillator is a better candidate to test the above predictions experimentally. Perforations in the separating wall between cells, working at different temperatures (and thus having different rate constants and therefore different periods13), were used by Marek14 as a coupling method. In this way, two coupled oscillators could become stationary. The temperature gradients formed and the unknown changes in the rate constants make any comparisons with theoretical predictions almost impossible. We have, therefore, chosen to repeat the experiment with a different coupling method, more amenable to calculations. Experimental Section The BZ reaction was run in parallel in two CSTR’s (continuously stirred tank reactor) at 25 OC. The final concentrations of the feed materials were 3 X 10-*M malonic acid (Merck 99%), M KBr03 (B.D.H., 99.9%), 3 X M Ce3+ (as 3 X Ce2(S04)3,Fluka, 99.8%), and various concentrations of KBr (Merck, 99.5%), all at 1.5 M sulfuric acid (Merck). The cell volume of 50 mL was fed a t the rate of 4.5 mL/min, i.e., ko = 1.5 X 10- s-l, by a multichannel peristaltic pump (Desaga AG.). The feed was 1.5 mL/min of each of three solutions containing (a) malonic acid and cerous ions, (b) bromate ions, or (c) bromide ions. The overflow was pumped out with the same peristaltic pump. The voltage between a Pt electrode (El-Hama Ltd.) and a Ag/AgCI double-junction reference electrode (Orion Research Inc.) was recorded. The coupling between the two C S T R s was achieved by transfering, with a second peristaltic pump, material from one CSTR to the second and vice versa. Different coupling rates were achieved by changing the pump speed and by using tubes of different diameter (0.1-0.23 cm). The length of the connecting tubes is about 80 cm. Results and Discussion Figure 1 shows a typical recording of the voltage at the two CSTR’s. As the coupling starts, the regular pattern of oscillations stops and the system becomes stable. Once the coupling is stopped, the oscillations resume. If the coupling rate becomes too small, the oscillations continue and no stability is achieved. There is a lag between the time the coupling is turned on (off) and the time the oscillations stop (start). This time lag depends among other things on the particular constraints of the two CSTRs (1.1) (a) K. Bar-Eli in ‘Non Linear Phenomena in Chemical Dynamics”, C. Vidal and A. Pacault, Ed%, Vol. 12, Springer-Verlag,Berlin, 1981, Springer Series in Synergetics, pp 228-239; (b) K. Bar-Eli and W. Geiseler, J. Phys. Chem., 87,3769 (1983); (c) W. Geiseler, Ber. Bunsenges. Phys. Chem., 86, 721 (1982); (d) W. Geiseler, J. Phys. Chem., 86,4394 (1982); (e) M. Orban, P. De Kepper, and I. R. Epstein, J. Am. Chem. Soc., 104, 2657 (1982). (12) K. Bar-Eli and J. Ronkin, J. Phys. Chem., 88, 2844 (1984). (13) M. Marek and I. Stuchl, Biophys. Chem., 3, 241 (1975). (14) M.Marek in ‘Synergetics: Far from Equilibrium“, A. Pacault and C. Vidal, Eds., Springer-Verlag, Berlin, 1979, p 12-17.
[Br-1, = 3
X lo-’ A
M“
CSTR I1 [Br-lo = 3 X lo-’ M’
coupling rate, mL/min 24
-
16 12
-
10
+
4
Br-1, = 1 X lo-) M
-
24
-
16 9.8
+ Br-1, = 3
X
+ + + +
M 24
+
16 9.8 4
OOnly the bromide ion concentration in the feed is given. Other feed concentrations are shown in the text. bThe plus sign means that oscillations continue while the minus sign means that oscillations stop, and steady state is achieved. ‘Both CSTRs oscillate when the coupling rate is zero, Le., no coupling.
and is clearly seen in the figure. In this range of constraints, the oscillation period changes very fast with bromide ion concentration. Slight differences in the properties of the (diameter or elasticity) leading tubes can cause the observed differences in the periods of the two CSTRs when the coupling is turned off. The calculations presented in earlier work1-) ignore the time the material spends in the interconnecting tubes. This time depends on the tubes diameter and pumping speed and is calculated to be of the order of a few seconds. This time is small compared to the oscillation period (about 2 min). The chemical changes occurring in the tubes are expected, therefore, to be small. Including these changes in the calculations will make them tremendously difficult (the computations will have to involve a batch part, in the tubes, and a CSTR part in the reaction vessels themselves). A preliminary study of the coupling rates which cause the stability is shown in Table I. As the coupling rate is small the oscillations continue; when the coupling rate is increased beyond a certain limit, the oscillations stop and stability is achieved. When the coupling is further increased one expects to resume the oscillations when the two CSTR’s will be essentially one. Such high coupling rates could not be achieved, however, with the present equipment. When the difference between the two CSTR’s increases, as in the last portion of Table I, one notices that one CSTR stops oscillating while the other one continues to do so. Such results can be obtained if the oscillation amplitude of one CSTR is much smaller than that of the other and thus will fall below the noise and will seem to stop. Indeed detailed calculations done on the coupling of NFT oscillators1v2*1’show the feasibility of such phenomenon (cf. Table I of ref 1 and Figure 1 of ref 2). Crowley and Field15report similar results when BZ oscillators are coupled electrically. In this way an effective transfer of cerium ions only from one CSTR to the next occurs. The coupling rate needed to create stability is roughly of the same order as the inflow rate. This is in agreement with the calculated results given Further work to evaluate more exact limits of stability as a function of the various constraints, the exact concentrations of the stable states at the two CSTRs (thus gaining an idea about the inhomogeneity of the system), proceeds in this laboratory. Registry No. Malonic acid, 141-82-2; bromate, 15541-45-4; cerium, 7440-45-1. ( 1 5) M. F. Crowley and R. J. Field in ‘Non Linear Phenomena in Chemical Dynamics”, C. Vidal and A. Pacault, Eds., Vol. 12, Springer-Verlag, Berlin, 1981, Springer Series in Synergetics, pp 147-153.
